Investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium crystals by the Czochralski method

Numerical investigation of the variations in the crystallization front shape during growth of gadolinium gallium and terbium gallium garnet crystals in the same thermal zone and comparison of the obtained results with the experimental data have been performed. It is shown that the difference in the behavior of the crystallization front during growth of the crystals is related to their different transparency in the IR region. In gadolinium gallium garnet crystals, which are transparent to thermal radiation, a crystallization front, strongly convex toward the melt, is formed in the growth stage, which extremely rapidly melts under forced convection. Numerical analysis of this process has been performed within the quasistationary and nonstationary models. At the same time, in terbium gallium garnet crystals, which are characterized by strong absorption of thermal radiation, the phase boundary shape changes fairly smoothly and with a small amplitude. In this case, as the crystal is pulled, the crystallization front tends to become convex toward the crystal bulk.     

A modeling approach for the non‐isothermal antisolvent crystallization of a solute with weak temperature dependent solubility

Antisolvent crystallization is a crystallization technique, which is normally operated isothermally. However, non‐isothermal operation is on occasions performed for solutes that have temperature dependent solubility. This paper shows that it is beneficial to operate antisolvent crystallizers non‐isothermally even for solutes whose solubility is weakly dependent on temperature. In this context, it demonstrates the joint control of particle mean size and size distribution coefficient of variation. A non‐isothermal crystallization model‐based framework is developed for the sodium chloride‐ethanol‐water system and validated for both isothermal and non‐isothermal operations. This framework was used to systematically determine both the optimal antisolvent feed rate and temperature profiles that minimize the coefficient of variation while producing a specified mean crystal size. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rapid crystal growth without inherent supersaturation induced by nanoscale fluid flows?

Crystal growth is a process that only takes place under non‐equilibrium conditions and a necessary prerequisite is that the crystal is exposed to a phase that is supersaturated in the material the crystal is composed of, be it a solution, a vapour or a supercooled melt. In industrial mass crystallization the growth rate for a population of crystals (in suspension growth processes [1]) rarely exceeds mean linear velocities of 10^‐7 ms^‐1. Here we present a mass crystallization process which is accompanied by rapid crystal growth several orders of magnitude faster and into a region of solution that is without inherent supersaturation. The material investigated is a solid hydrate that exhibits a solution mediated phase transition to its anhydrous form in the presence of methanol [2]. The phase transition is initiated simply by placing an amount of hydrate crystals into the solvent and is characterized by the rapid emergence of needle‐shaped crystals. The needles emanate from the crystal faces of the hydrate crystals and grow into the solution, which is nominally free of the substance to be crystallized. The high growth rate of the crystals, which of the order of up to 10^‐4 ms^‐1 is surprising. Although rapid needle growth has been observed before [3‐9], to date a satisfactory explanation for needles growing under the abovementioned conditions is still outstanding. Based upon the topology of the crystals we propose a tentative mechanism for this phenomenon capable of explaining the unusually rapid growth and highlight those questions that need addressing in order to verify this mechanism. X‐ray powder diffraction is used to characterize the crystal phase of the needles; confocal fluorescence microscopy reveals that the needles are hollow. The width of these needles is between 0.5 and 5 μm, their length appears to be limited only by the amount of hydrate available for their formation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reducing Inversion Twinning in Single Crystal Growth of GaPO4

Gallium orthophosphate (GaPO₄) single crystals were grown by the reverse temperature gradient method from phosphoric acid solutions under hydrothermal conditions. Twins after (110) were studied by etching faces having been cut perpendicular to one of the twofold axes. Based on the determination of the twin boundary position as well as on the knowledge of the growth rates of different crystallographic forms, a few faces have been chosen to be quite promising for growing high‐quality GaPO₄ single crystals if they are offered at the referring seed crystal. From the characterization of the grown crystals conditions have been found, which may lead to the reduction of the inversion twin number during the growth process.     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.     

水平结晶法生长蓝宝石晶体的热交换研究

本文通过综合处理结晶设备内部(含有晶体的容器里)和外部(设备的工作空间:加热件和热绝缘)的热交换问题,给出了对不同类型结晶设备热系统的计算研究.数学模型计算的结果与用水平定向结晶设备生长蓝宝石板的实验作了比较,描述了实验发现的温场突变现象,并就水平定向生长蓝宝石晶体分析了它产生的可能原因.给出了模型准确性和应用范围的结论.     

DTA peak shift studies of primary crystallization in glasses

Following the recognition during the last decade that knowledge of the shift in the exothermic crystallization DTA peak as a function of pre-DTA isothermal heat-treatment times and temperatures, can provide quantitative information about the crystallization kinetics, there has been renewed interest in DTA investigations of crystallization of glasses. Most studies to date, however, have focussed on the kinetics of polymorphic crystallization (where the compositions of the crystal and the parent glass are the same). These studies have established that the DTA peak shifts to lower temperatures with increased pre-DTA heat-treatment times and JMAK-based formalisms have been developed to extract the steady state nucleation rate from the DTA peak shift data. In this paper, we report new results on the DTA peak shift in systems undergoing primary crystallization (where the compositions of the crystal and glass are different). The DTA results show that the exothermic peak temperature decreases initially but increases later on, becoming significantly larger than the initial value, with increase in the pre-DTA heat-treatment time at a fixed temperature. This increase at long times has not been reported previously and is qualitatively different than the monotonic decrease reported for polymorphic crystallization. To rationalize these new results, a model of primary crystallization has been developed which includes homogeneous nucleation, diffusion-controlled growth, Gibbs-Thomson effect, and a mean field soft-impingement correction during growth. Based on this model and experimental results, it is concluded that the initial shift to lower temperatures is due to an increase in the number of nuclei (as concluded previously by others for the case of polymorphic crystallization) and the later shift towards high temperatures in our experiments is due to diffusion-controlled growth during the pre-DTA heat treatment.     

The Effect of Free Convection on Solid/Liquid Interface in the Czochralski Crystal Growth Method

This paper regards the interaction of free and forced convection in the Czochralski configuration. A relationship between the crystal rotation rate and growth parameters at which the crystallization front remains flat, at which the crystallization front remains almost flat, has been studied. This relationship is compared with experimental data.     

Perfection and homogeneity of space-grown GaSb:Te crystals

A Te-doped GaSb crystal grown by the method of directed crystallization under microgravitation has been studied by X-ray topography. It is shown that the structural perfection of the crystal part grown without contact with the ampule walls is substantially higher than the structural perfection of the crystals grown under terrestrial conditions. The distribution of a Te dopant in the crystal is studied by quantitative X-ray topography, and it is shown that, if the gap between the growing crystal and the ampule is small, the Marangoni convection in the melt can be less intense than the convection provided by residual microgravitation. The relation between the formation of a flat face on the crystallization front (faceting) and the formation of twins is also established.     

Growth spirals of gadolinium gallium garnet (GGG) crystals

Slices cut from various locations in two GGG spirals grown by the Czochralski method have been studied using double crystal X-ray topography. In selected regions of the slices the lattice parameter has been measured by a modified Bond method. An increase of lattice parameter has been found in the outer part of the crystal where growth bands have smaller periodicity than those in the central region of the spiral. An analysis of crystallization front changes allowed us to suppose that the asymmetry of the heat field around the growing crystal, and the forced convection of the melt, are responsible for the crystal's growing in the shape of a spiral.     

Effect of the Temperature Fluctuation of the Melt on β‐BaB2O4 (BBO) Crystal Growth

In this paper the effect of the growth temperature fluctuation, for instance, the transient furnace temperature variation due to a short‐term electric power supply interruption on BBO crystal growth was investigated based on the theory of temperature wave transmitting in melt and the boundary layer theory of melt. It was found that the critical width of the temperature pulse to avoid the temperature wave penetrating through the boundary layer and reaching to the growth interface at a constant rotation speed (9∼4 r/min) is 69∼150 s and the corresponding amplitude of the temperature pulse is high more than 60 °C due to the large thickness of the velocity boundary layer of the melt. This result indicates that a small transient temperature fluctuation has no significant effect on the crystal quality, and therefore implies that not only transport processes but interface growth kinetics, a two‐dimensional nucleation growth mode at the interface may also dominate the crystal growth.     

Process design for the shape control of crystals grown by Kyropoulos or SAPMAC method

A mathematical model has been proposed to design the process for growing a shaped crystals by Kyropoulos method or SAPMAC method. Crystal shape evolution behaviours under various processes were analysed. The results show that the crystal would go through a transitory shoulder‐expanding stage after which the crystal diameter rapidly decreases under a constant pulling rate and a constant heater temperature. Reducing pulling rate and heater temperature could depress the decrease of crystal diameter after the shoulder‐expanding stage so that enhance the length of crystal. However, the crystal diameter is more sensitive to pulling rate than to heater temperature, and an equal‐diameter crystal can not be grown in non‐undercooled melt by soley reducing the heater temperature. That means that adjusting the pulling rate is the most effective and convenient approach for controlling crystal diameter evolution and simultaneously decreasing both the pulling rate and the heater temperature is the optimal process for growing an equal‐diameter crystal. Moreover, a numerical approach for quantifactional designing crystal shape and corresponding growth processes was proposed according to the model, an example of crystal shape design was given out. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Initial stages of SiC crystal growth by PVT method

Initial stages of SiC crystal growth by Physical Vapor Transport method were investigated. The following features were observed: (a) many nucleation crystallization centres appeared on the seed surface during the initial stage of the growth, (b) at the same places many separate flat faces generated on the crystallization front, (c) the number of facets was dependent on the shape of the crystallization front and decreased during growth, (d) appearance of many facets lead to decrease of structural quality of crystals due to degradation of regions where crystallization steps from independent centres met. The results revealed that the optimal crystallization front should be slightly convex, which permits the growth of crystals with single nucleation centre and evolution of single facet on the crystallization front. The subjects of study were the shape and the morphology of growth interface. Defects in the crystallization fronts and wafers cut from the crystals were studied by optical microscopy, atomic force microscopy (AFM) combined with KOH etching and X‐ray diffraction. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the bending radius and diffraction profile parameters for X-Ray Analyzer Crystals with X-ray parallel beam

A technique is proposed based upon angular scanning of a bent crystal shifted from the rotation axis. The axis-to-crystal distance providing the maximum reflecting efficiency is used to determine the bending radius of reflecting planes, and the diffraction profile can be obtained using an efficiency variation with a crystal shift tangential to Rowland circle at front focus. A rocking curve plotted — a “topogram” of the crystal surface is used to measure its reflecting area and a regularity of bending. The technique is suitable for various types of analyzers in both the reflecting and transmitting arrangements. Instrumental conditions are defined and some experimental examples are given.     

Measurement of three‐dimensional concentration gradients around a crystal growing from its aqueous solution using laser schlieren

Schlieren measurements of the gradients of the concentration field around a KDP crystal growing from its aqueous solution are reported. The measurement of the concentration gradient field is important for crystal growth because it controls the rate of solute transport from the bulk of the solution to the crystal surface. In the crystal vicinity, the concentration gradients have a three dimensional distribution. The concentration gradient field has been imaged using monochrome schlieren technique. Four view angles, namely 0, 45, 90 and 135° have been utilized. By interpreting the schlieren images as projection data of solute concentration gradient, the three‐dimensional concentration gradient field around the crystal has been determined using an algebraic reconstruction technique. At low supersaturation levels, the growth process is accompanied by weak fluid movement during which diffusion effects are significant. At higher levels of supersaturation and large crystal size, a well‐defined convective plume around the growing crystal is observed. Reconstruction of concentration gradients around the crystal explains the preferential growth rates of various faces of the crystal. The non‐circular shape of the crystal is seen to affect the symmetry of the distribution of concentration gradients in its vicinity. The effect of crystal morphology on the orientation of convection currents rising from the crystal surface has also been brought out on the basis of the reconstructed concentration gradients distribution in the growth chamber. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 10¹² not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10¹⁰. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.     

Correlation of the structural imperfection and morphology of Bi<Subscript>4</Subscript>Ge<Subscript>3</Subscript>O<Subscript>12</Subscript> crystals grown by the low-gradient Czochralski method

This paper reports on the results of investigations into the morphological structure of the facets of Bi₄Ge₃O₁₂ crystals grown by the Czochralski method under the conditions of low temperature gradient (0.1–1 K/cm). A correlation between the morphological features of the facets at the crystallization front and the formation of defects in the bulk of the crystal is revealed. It is demonstrated that the {112} facets remain regular while the growing surface deviates from the (112) crystallographic plane by an angle of up to 1°. At larger deviations, there occurs a crossover from the stable facet growth to the growth of macrosteps or normal growth depending on the growth conditions.     

White and Taylor Type Guest Host Displays Without Scattering Effects Using the Tilted Boundary Conditions

White and Taylor type guest host displays using the tilted boundary condition have been reported. The parallel or the perpendicular boundary condition is usually used for these displays and both conditions cause scattering phemomena after the electric field removal. The present paper reports the relaxation processes of samples with the tilted boundary after the field removal. Using the tilted boundary, two types of nonscattering conditions depending on the thickness of the liquid crystal layer (d), the natural pitch (Po) and the boundary condition (φ) exist. Both types of conditions are discussed in detail.     

Kinetical study of the nonstoichiometric vapour growth process in the system ZnSe:I2

We have studied the growth of ZnSe crystals by chemical transport in a closed system in nonstoichiometric conditions, and we have deduced that the interface kinetics is the phenomenon limiting the growth process. The effect on the growth process of the deviation from stoichiometry of the II‐VI compound was investigated using a mathematical model that involves indirect data computed from directly obtained experimental values. The experimental crystallization rate was compared with the maximum value of the transport flux calculated using the Arizumi‐Nishinaga model. The influence of the stoichiometry of the source material and of the variations in the growth parameters (supercooling, geometrical dimension, specific loading of the ampoule and iodine concentration) on the ZnSe crystal growth process has also been studied. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of zeolite ZSM‐5: Effect of emulsifiers

Zeolite ZSM‐5 has been synthesized in presence of various emulsifiers. Influence of types and proportions of cationic, anionic and non‐ionic emulsifier has been studied. Cationic emulsifier, cetyl trimethyl ammonium bromide resulted in an amorphous phase, whereas anionic emuisifier, sodium lauryl sulphate afforded crystalline phase, identified as magadiite. Non‐ionic emulsifiers, 1,2,3‐benzotriazole and sorbital mono‐stearate led to the formation of pure crystalline ZSM‐5 phase. Emulsifier concentration was found to affect the process of crystallization, and the crystal size and morphology of ZSM‐5. Emulsifier necessitated higher crystallization temperature and/or longer hydrothermal period. ZSM‐5 crystallization was observed to proceed through magadiite phase formation. In case of benzotriazole, unusual stacked square platelet type morphology and with sorbital monostearate, very small crystals were observed.